On implementing a primal–dual interior-point method for conic quadratic optimization

Based on the work of the Nesterov and Todd on self-scaled cones an implementation of a primal–dual interior-point method for solving large-scale sparse conic quadratic optimization problems is presented. The main features of the implementation are that it is based on a homogeneous and self-dual model, it handles rotated quadratic cones directly, it employs a Mehrotra type predictor–corrector extension and sparse linear algebra to improve the computational efficiency. Finally, the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems. This is a novel feature for our implementation. Computational results are also presented to document that the implementation can solve very large problems robustly and efficiently.